CN117388574A - High-frequency harmonic analysis method, system, equipment and storage medium based on MSD hybrid convolution window - Google Patents
High-frequency harmonic analysis method, system, equipment and storage medium based on MSD hybrid convolution window Download PDFInfo
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Abstract
The invention discloses a high-frequency harmonic analysis method, a system, equipment and a storage medium based on an MSD hybrid convolution window, which comprises the following steps: sampling a voltage and current signal x (n) to be measured in the wireless charging process, wherein the sampling rate of the signal is f s Obtaining N-point sampling data after analog-to-digital conversion; constructing an MSD window function and performing mixed convolution operation to obtain a mixed convolution window; adding MSD mixed convolution window to the sampled N-point sampling data to obtain FFT spectrum; determining four spectral lines in the four-spectral line interpolation based on the FFT spectrum; and obtaining the frequency amplitude and the phase of the corrected fundamental wave and each subharmonic through interpolation operation. The invention improves the precision of harmonic measurement and analysis; more haveFrequency spectrum leakage is effectively suppressed, and frequency resolution is improved; and a four-spectral-line interpolation algorithm is adopted, so that errors caused by a fence effect are reduced.
Description
Technical Field
The invention relates to the technical field of harmonic analysis, in particular to a high-frequency harmonic analysis method, a system, equipment and a storage medium based on an MSD hybrid convolution window.
Background
With the rapid development of electric automobiles, wireless charging can effectively overcome the defects of a wired charging mode, and is receiving more and more attention. The current mainstream wireless charging method is still electromagnetic induction type, the research is earliest, the research is deepest, researchers are most, the standard is also spreading gradually, but in the aspect of current testing, because the wireless charging frequency is higher, 85kHz is commonly adopted at present, the testing difficulty is that the power consumption of an AC-AC end, the efficiency testing is carried out, the amplitude phase angle of an electric signal is the most basic measurement quantity, and the accuracy is very important. Meanwhile, as wireless charging is an emerging industry, harmonic analysis of high-frequency electric signals is in a blank state at present, and most harmonic processing methods are concentrated on the power frequency condition.
The Fast Fourier Transform (FFT) is currently one of the most prominent algorithms for harmonic analysis in the power grid band, since it is simple and easy to implement in embedded systems and can therefore be applied to high frequency power measurements. However, the signals are dynamic and difficult to synchronously sample in the wireless charging process, so if the FFT is directly used for harmonic detection, spectrum leakage and fence effect can occur, and harmonic parameters cannot be accurately calculated, so a windowing algorithm is adopted, a self-convolution window function is better than a classical single window function in suppressing spectrum leakage, but the window function multi-order convolution operation also causes the problem of large calculation amount, and the accuracy of harmonic detection is affected. Therefore, how to provide a high-frequency harmonic analysis method with high precision becomes a technical problem to be solved.
The maximum sidelobe attenuation (Maximum Sidelobe Decay, MSD) window has the fastest sidelobe attenuation speed under the condition of the same term number, can obviously reduce spectrum leakage, and is beneficial to improving the precision of harmonic measurement and analysis. Meanwhile, the mixed convolution window can better inhibit spectrum leakage and improve frequency resolution.
Disclosure of Invention
The invention aims to: the invention aims to provide a high-frequency harmonic analysis method, a system, equipment and a storage medium based on an MSD hybrid convolution window, which effectively solve the problems of large spectrum leakage and low spectrum analysis accuracy caused by poor side lobe characteristics of a cosine window in a fast Fourier transform harmonic analysis method.
The technical scheme is as follows: the analysis method provided by the invention comprises the following steps:
(1) Sampling a voltage and current signal x (n) to be measured in the wireless charging process, wherein the sampling rate of the signal is f s Obtaining N-point sampling data after analog-to-digital conversion;
(2) Constructing an MSD window function and performing mixed convolution operation to obtain a mixed convolution window;
(3) Adding MSD mixed convolution window to the sampled N-point sampling data to obtain FFT spectrum;
(4) Determining four spectral lines in the four-spectral line interpolation based on the FFT spectrum;
(5) And obtaining the frequency amplitude and the phase of the corrected fundamental wave and each subharmonic through interpolation operation.
Further, the method for constructing the MSD window function in the step (2) is as follows:
selecting MSD windows of different lengths according to equation (1), i.e. w 1 (m 1 )，w 2 (m 2 )，...，w p (m p )，
Corresponding length M 1 ，M 2 ，...，M p ，
Further, the method for determining the mixed convolution window in the step (2) is as follows:
the mixed convolution window function time domain obtained after carrying out convolution operation on MSD cosine windows with different lengths is as follows:
0 s are added at the first segment or the tail end of the sequence, so that the length of the mixed convolution window
Performing FFT (fast Fourier transform) on the time domain signal convolution result of the formula (1) to obtain a frequency domain signal convolution result of a p-order mixed convolution window of the formula (3):
further, the method for obtaining the FFT spectrum based on the mixed convolution window in the step (3) includes:
p-order mixed convolution window w with length N after discrete signal sampling hp (n) obtaining a windowed signal:
x wp (n)＝x(n)w hp (n) (4)
fourier transforming equation (3) to obtain the frequency domain of the windowed signal:
wherein the frequency of the sampling signal x (n) is f 0 Amplitude is A, initial phase isNeglecting the effect of side lobes at the negative frequency point, the method can obtain:
bringing formula (2) into availability:
the window function expressions for each participating convolution are:
the mixed convolution window expression is obtained from equation (8):
further, the method for determining four spectral lines in the four spectral line interpolation in the step (4) is as follows:
selecting spectral line k with maximum amplitude near peak spectral point f in FFT spectrum with frequency close to peak spectral point f after grid signal x (n) windowing 2 、k 2 The next largest spectral line k 1 、k 4 Let the amplitude of the two phases be y respectively 1 、y 2 、y 3 、y 4 I.e. y 1 ＝|X wp (k 1 )|、y 2 ＝|X wp (k 2 )|、y 3 ＝|X wp (k 3 )|、y 4 ＝|X wp (k 4 )|，
The corresponding magnitudes for each spectral line are as follows:
further, the method for determining the frequency amplitude and phase of the fundamental wave and each subharmonic wave after correction in the step (5) is as follows:
let δ=k-k 2 -0.5, since 0.ltoreq.k-k 2 If not more than 1, delta is less than-0.5, 0.5]Establishing four spectral line interpolation to solve the offset delta,
i.e.Gamma is a function of delta, and gamma=h (delta), and the offset is obtained by solving an inverse function of the gamma=h (delta) through least square fitting:
δ＝H -1 (γ) (12)
fitting by using a polynomial approximation method to obtain:
δ≈L(γ)＝a 1 γ+a 3 γ 3 +…+a 2q+1 γ 2q+1 (13)
wherein a is 1 ，a 3 ，…，a 2q+1 Odd term times.
The frequency correction formula according to the delta-obtainable signal is:
f 0 ＝kΔf＝(k 2 +0.5+δ)f s /N (14)
the phase correction formula of the signal is:
the amplitude correction formula of the signal is:
when N is large, the magnitude correction formula is expressed by a fitting formula τ (δ) as:
where τ (δ) is an even function, the correction polynomial of the magnitude is:
wherein a is 0 ，a 2 ，…，a 2q Is an even term coefficient.
Further, the polynomial approximation is to fit an inverse function offset using a polyfit function of Matlab.
Further comprises a data acquisition module, a windowing processing module and an output module,
the data acquisition module acquires wireless charging current and voltage data of the electric automobile and changes the voltage and current data into discrete signals;
the windowing processing module performs windowing processing on the acquired voltage and current data to obtain a windowed FFT spectrum:
and the output module obtains interpolation coefficients from the data by adopting a four-spectral-line interpolation algorithm, and corrects the data to obtain corrected voltage current phase amplitude and frequency.
Further, a memory for storing instructions for a computer to perform the analysis method of any one of claims 1-7 and a processor for executing instructions for the computer-executable analysis method of any one of claims 1-7 are included.
Further, the computer readable storage medium stores computer executable instructions that when executed by a processor implement the MSD hybrid convolution window-based high frequency harmonic analysis method of any one of claims 1-7.
The beneficial effects are that: compared with the prior art, the invention has the following remarkable advantages: the frequency spectrum leakage is obviously reduced by using a maximum sidelobe attenuation (MSD) window of the fastest sidelobe attenuation speed under the condition of the same term number, and the precision of harmonic measurement and analysis is improved; by adopting the mixed convolution window, the main lobe size of the mixed convolution window depends on the minimum main lobe of the convolved window function, and the side lobe attenuation speed is the sum of the attenuation speeds of a plurality of convolved windows, so that the frequency spectrum leakage can be more effectively restrained, and the frequency resolution can be improved; and a four-spectral line interpolation algorithm is adopted, so that errors caused by a fence effect are reduced.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of amplitude versus error versus time;
FIG. 3 is a phase versus error plot;
FIG. 4 is a frequency versus error plot;
FIG. 5 is a graph of amplitude error based on a 5/6MSD window with frequency fluctuations;
FIG. 6 is a graph of phase error based on a 5/6MSD window with frequency fluctuations;
FIG. 7 is a graph of frequency error based on a 5/6MSD window with frequency fluctuations;
FIG. 8 is a graph of fundamental amplitude measurement error under white noise;
fig. 9 is a diagram of fundamental wave phase measurement error under white noise:
fig. 10 is a graph of fundamental frequency measurement error under white noise.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
Example 1
As shown in fig. 1, the high-frequency harmonic analysis method of the present invention specifically includes the following implementation steps:
(1) Sampling a voltage and current signal x (n) to be measured in the wireless charging process, wherein the sampling rate of the signal is f s Obtaining N-point sampling data after analog-to-digital conversion;
(2) Constructing an MSD window function and performing mixed convolution to obtain a mixed convolution window;
(3) Adding MSD mixed convolution window to the sampled N-point sampling data to obtain FFT spectrum;
(4) Determining four spectral lines in the four-spectral line interpolation based on the FFT spectrum;
(5) And obtaining the frequency amplitude and the phase of the corrected fundamental wave and each subharmonic through interpolation operation.
In the step (2), the method for constructing the mixed convolution window is as follows:
the method for constructing the MSD window function is as follows:
wherein 4 to 6 items a l The details of the parameters of (2) are shown in Table 1.
Table 1: 4-6 MSD window function coefficient a l
Taking two MSD windows of different lengths, i.e. w 1 (m 1 )，w 2 (m 2 ) Corresponding length M 1 ，M 2 Mixed convolution window obtained by convolving cosine windowsThe functional time domain result is:
w hp (n)＝w 1 (m 1 )*w 2 (m 2 ) (2)
0 s are added at the first segment or the tail end of the sequence, so that the length of the mixed convolution window
Performing FFT (fast Fourier transform) on the time domain signal convolution result of the formula (1) to obtain a frequency domain signal convolution result of a 1-order mixed convolution window shown in the formula (3):
W hp (ω)＝W 1 (ω)*W 2 (ω) (3)
in the step (3), the method for obtaining the FFT spectrum of the voltage-current signal x (n) after windowing based on the mixed convolution window is as follows:
1-order mixed convolution window w with length N after discrete signal sampling hp (n) obtaining a windowed signal result of:
x wp (n)＝x(n)w hp (n) (4)
performing Fourier transform on the formula (3) to obtain a frequency domain expression of the windowed signal, wherein the frequency domain expression is as follows:
wherein the frequency of the sampling signal x (n) is f 0 Amplitude is A, initial phase is
Neglecting the effect of side lobes at their negative frequency points can be obtained:
bringing formula (2) into availability:
the window function expressions for each participating convolution are:
the mixed convolution window expression is obtained by the formula (8)
In the step (4), the method for determining four spectral lines in the four spectral line interpolation is as follows:
considering the signal frequency f when affected by non-integer harmonics s With Δf×n, it is difficult to locate at the sampled frequency point, i.e. k is generally not an integer, and spectral line k with frequency close to maximum amplitude near peak spectral point f in FFT spectrum after windowing of grid signal x (N) is selected 2 、k 2 The next largest spectral line k 1 、k 4 Let the amplitude of the two phases be y respectively 1 、y 2 、y 3 、y 4 I.e. y 1 ＝|X wp (k 1 )|、y 2 ＝|X wp (k 2 )|、y 3 ＝|X wp (k 3 )|、y 4 ＝|X wp (k 4 )|。
The corresponding amplitude of each spectral line is specifically as follows:
in the step (5), the specific method for obtaining the frequency amplitude and phase of the corrected fundamental wave and each subharmonic is as follows:
let δ=k-k 2 -0.5, since 0.ltoreq.k-k 2 If not more than 1, delta is less than-0.5, 0.5]And establishing four spectral line interpolation to solve the offset delta.
I.e.Gamma is a function of delta, and gamma=h (delta), and the offset is obtained by solving an inverse function of the gamma=h (delta) through least square fitting:
δ＝H -1 (γ) (12)
a polynomial approximation method is adopted for calculation, an inverse function is fitted by utilizing a polynt function of Matlab,
fitting can be obtained:
δ≈L(γ)＝a 1 γ+a 3 γ 3 +…+a 2q+1 γ 2q+1 (13)
wherein a is 1 ，a 3 ，…，a 2q+1 Odd term times.
And obtaining delta, wherein a frequency correction formula of the available signal is as follows:
f 0 ＝kΔf＝(k 2 +0.5+δ)f s /N (14)
the phase correction formula of the signal is:
the amplitude correction formula of the signal is:
when N is large, the magnitude correction formula can be further expressed by the fit formula τ (δ):
where τ (δ) is an even function, the correction polynomial of the magnitude is:
a 0 ，a 2 ，…，a 2q is an even term coefficient.
Side lobe spectrum leakage in the existing spectrum leakage is mainly caused by window functions, and if frequency leakage is to be reduced, window functions with excellent spectrum characteristics, particularly window functions with excellent side lobe characteristics, need to be selected; for a single window function, the window function with a narrower main lobe tends to have poorer side lobe characteristics, while the window function with a better side lobe performance tends to have wider main lobe, so that the window function is difficult to achieve multiple consideration. The convolution algorithm is to convolve a plurality of windows on a frequency domain, and the obtained convolution window has better frequency spectrum performance. The self-convolution window function is better than the classical single window function in suppressing spectrum leakage, but the window function multi-order convolution operation also causes the problem of large calculation amount, and the accuracy of harmonic detection is affected. The invention obviously reduces the frequency spectrum leakage by using the maximum side lobe attenuation (MSD) window of the fastest side lobe attenuation speed under the same term number, and improves the precision of harmonic measurement and analysis; by adopting the mixed convolution window, the main lobe size of the mixed convolution window depends on the minimum main lobe of the convolved window function, and the side lobe attenuation speed is the sum of the attenuation speeds of a plurality of convolved windows, so that the frequency spectrum leakage can be more effectively restrained, and the frequency resolution can be improved; and a four-spectral line interpolation algorithm is adopted, so that errors caused by a fence effect are reduced.
Example 2
The procedure for establishing several hybrid convolution window correction formulas is as follows:
the method for constructing the MSD window function is as follows:
wherein 4 to 6 items a l The details of the parameters of (2) are shown in Table 1.
Substituting the above formula into the first-order mixed convolution window frequency domain expression W h2 (ω)＝w 1 (m 1 )*w 2 (m 2 ) The frequency domain expression for obtaining the 4-term/5-term MSD mixed convolution window (hereinafter referred to as 4/5MSD window) function and the 5-term/6-term MSD mixed convolution window (hereinafter referred to as 5/6MSD window) function is as follows:
and calculating by adopting a polynomial approximation method, and obtaining delta and tau (delta) corresponding to each window function through fitting a polyfit function of Matlab.
Hanning window four lines:
δ＝1.130136160107520γ+0.184133500469901γ 3 +0.071461995030240γ 5 +0.048205375940325γ 7 (20)
τ(δ)＝1.070997483475462+0.275923374023576δ 2 +0.044610433915516δ 4 +0.005798366080202δ 6 (21)
4 th order MSD window four spectral lines:
δ＝2.375409829331954γ+0.434788170025496γ 3 +0.191128752108198γ 5 +0.117437235549368γ 7 (22)
τ(δ)＝1.344567506038478+0.242047602646459δ 2 +0.023789207125749δ 4 +0.001738503716104δ 6 (23)
5 th order MSD window four spectral lines:
δ＝2.984407482980075γ+0.554356548164331γ 3 +0.246894355902731γ 5 +0.150148675986871γ 7 (24)
τ(δ)＝1.466274048647414+0.225432967313756δ 2 +0.018557584770171δ 4 +0.001112251266950δ 6 (25)
6 th order MSD window four spectral lines:
δ＝3.590387374060534γ+0.672500205378279γ 3 +0.301612706194318γ 5 +0.182413490826130γ 7 (26)
τ(δ)＝1.579386618623500+0.211361007245151δ 2 +0.014961501031750δ 4 +0.000760087705187δ 6 (27)
4/5MSD window four spectral lines:
δ＝5.042S77925326573γ+0.933908699775251γ 3 +0.412684790836807γ 5 +0.242361529254304γ 7 (28)
τ(δ)＝0.0169996931685023+0.00172876265972034δ 2 +0.0000915399157297752δ 4 +0.00000341079156483171δ 6 (29)
5/6MSD window four spectral lines:
δ＝6.25796687923816γ+1.17245734971182γ 3 +0.523816880884597γ 5 +0.309559818108644γ 7 (30)
τ(δ)＝0.0211328780717370+0.00178584699362194δ 2 +0.0000779395737720484δ 4 +0.00000236809544444061δ 6 (31)
example 3
As shown in fig. 2, 3 and 4, the 11 th order power harmonic signal was used for analysis.
Wherein the frequency of the sampling signal x (n) is f 0 Amplitude is A, initial phase isFor the fundamental frequency of the signal, 85.1kHz was taken. Sampling frequency f s For 2MHz, the other parameter settings are shown in table 2.
Table 2: amplitude and phase parameters of each subharmonic of power harmonic signal
The method and other classical window functions of the invention are used for respectively analyzing the electric power harmonic signals and comparing the electric power harmonic signals with the analysis results of the classical window functions, and the method and the other classical window functions are concretely as follows:
(1) Harmonic signal error analysis and comparison
As shown in fig. 2, 3 and 4, the errors of the amplitude, the phase and the frequency of the 4 MSD windows are all the highest; the errors of the 4/5MSD window and the 5/6MSD window are very small, which indicates that the mixed convolution can effectively improve the error precision; the 5/6MSD window is most prominent in the error performance of the three, and is minimum in the amplitude, phase angle and frequency error of the fundamental wave.
In terms of amplitude, the amplitude error of the 5/6MSD window is minimal, at 10 -10 ％～10 -8 % fluctuation, 0.5 order of magnitude lower than the 4/5MSD window, 2 order of magnitude lower than the Hanning window, and obviously lower than the errors measured by other single windows; in terms of phase, the amplitude error of the 5/6MSD window is minimal, at 10 -12 ％～10 -10 % fluctuation, higher error precision, and only higher than 4/5MSD window in 7 times and 11 times harmonic error, which is nearly 6 orders of magnitude lower than the Hanning window; in terms of frequency, the errors of the 4/5MSD window and the 5/6MSD window are small, and the errors are difficult to identify and become 0, so that the frequency errors of all the harmonics cannot be completely identified from fig. 6, but the frequency errors of the 1-3 th harmonic are all lower than the 5/6MSD window, and are about 5 orders of magnitude lower than the Hanning window in the case of fundamental waves. It can be seen that the 5/6MSD window has excellent performance in harmonic signal amplitude, phase and frequency detection accuracy.
(2) Harmonic analysis at fundamental frequency fluctuations
In the wireless charging process, the frequency is changed continuously due to the problems of battery performance change, coil heating and the like, and generally fluctuates around 85 kHz. The frequency is changed to change the frequency spectrum leakage, so that the research on the detection precision of the harmonic detection algorithm under the condition of frequency fluctuation is also one of important bases for judging the performance of the detection algorithm. Taking the sampling frequency f s 2MHz, 16384 sampling points, 84.5 kHz-85.5 kH frequencyz, 100Hz apart. The amplitude, phase and frequency error of the detection signal when the fundamental wave frequency fluctuates are shown in fig. 5, 6 and 7.
From fig. 5 to 7, the data of the errors at different fundamental frequencies are analyzed separately. In terms of amplitude, when the fundamental wave frequency fluctuates around 85kHz, the algorithm still has very high harmonic amplitude detection precision, and the amplitude error of each subharmonic is 10 -9 % order of magnitude and below, the change is stable, is far higher than national standard, and when the frequency deviation is great, the detection precision of each subharmonic amplitude is not reduced. In terms of phase, the phase error of each subharmonic of the chapter algorithm is 10 -9 % order of magnitude and below, has very high harmonic phase detection precision, and each subharmonic phase error has very good stability under the condition of different fundamental wave frequencies, and meanwhile, when the frequency deviation is large, the amplitude detection precision of each subharmonic is not reduced. In terms of frequency, the frequency error of each subharmonic of the chapter algorithm is 10 -15 % order of magnitude and below, has very high harmonic frequency detection accuracy.
In summary, when the fundamental wave frequency fluctuates around 85kHz, the precision of each signal parameter is not greatly reduced, the error is kept in a lower range, and the amplitude, phase, frequency and other information of each subharmonic of the power signal can still be accurately measured.
(3) Algorithm simulation of white noise addition
In the actual operation of wireless charging of an electric automobile, noise generated by various factors such as electricity, magnetism and heat in the environment can interfere harmonic detection, so that the detection result is greatly different from the actual value. In order to test the noise interference resistance of the four-spectral-line FFT interpolation algorithm with the 5/6MSD window, gaussian white noise with different signal to noise ratios is added to the signal, wherein the range is 20 dB-200 dB, and the interval is 20dB. Sampling frequency f s =2 MHz, the number of sampling points n=16384, the fundamental frequency f 1 Three algorithms detect the amplitude, phase, frequency error of the signal fundamental when the power signal is white noise at =85.1 KHz as shown in fig. 8, 9 and 10.
As can be seen from fig. 8 to 10, when the signal-to-noise ratio is small and the noise interference is large, the harmonic detection performance of each algorithm is limited, and as the signal-to-noise ratio increases, the detection precision of each algorithm is greatly improved, and the 5/6MSD window four-spectral line FFT algorithm can maintain a certain harmonic detection precision when the signal-to-noise ratio is small. Under the interference of white noise with different signal to noise ratios, the detection performance of the amplitude, the phase and the frequency of the white noise is superior to that of other two algorithms. Therefore, the 5/6MSD window four-spectral-line FFT algorithm has stronger anti-noise interference capability.
The 5/6MSD window has the excellent characteristics of minimum side lobe and steepest descent, has good inhibition on spectrum leakage, combines more accurate interpolation effect of four spectral line interpolation, and reduces errors caused by fence effect on detection.
The present embodiment also provides a high-frequency harmonic analysis system based on an MSD hybrid convolution window, including:
the data acquisition module is used for acquiring electric parameters of current and voltage of the electric automobile during wireless charging through the voltage transformer and the current transformer;
the windowing processing module is used for carrying out windowing processing on the acquired voltage and current data to obtain a windowed FFT spectrum:
and the output module is used for obtaining interpolation coefficients by adopting a four-spectral line interpolation algorithm to the data, and carrying out correction processing on the data to obtain corrected voltage current phase amplitude and frequency.
In a third aspect, embodiments of the present invention provide a computing device comprising:
a memory and a processor;
the memory is configured to store computer-executable instructions that, when executed by the one or more processors, cause the one or more processors to implement a high frequency harmonic analysis method based on an MSD hybrid convolution window according to any one of the embodiments of the present invention.
In a fourth aspect, embodiments of the present invention provide a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the MSD hybrid convolution window-based high-frequency harmonic analysis method.
The embodiment also provides a computing device, which is suitable for the case of the high-frequency harmonic analysis method based on the MSD hybrid convolution window, and comprises the following steps:
a memory and a processor; the memory is used for storing computer executable instructions, and the processor is used for executing the computer executable instructions to realize the high-frequency harmonic analysis method based on the MSD hybrid convolution window according to the embodiment.
The computer device may be a terminal comprising a processor, a memory, a communication interface, a display screen and input means connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The communication interface of the computer device is used for carrying out wired or wireless communication with an external terminal, and the wireless mode can be realized through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
The present embodiment also provides a storage medium having stored thereon a computer program which, when executed by a processor, implements a high frequency harmonic analysis method based on an MSD hybrid convolution window as proposed in the above embodiments.
Aiming at the defect of harmonic detection in the wireless charging process of an actual electric automobile, the invention applies a power frequency harmonic detection method to high-frequency electric energy detection, provides a four-spectral line interpolation FFT algorithm based on a 5/6MSD window, deduces a corresponding harmonic parameter calculation formula, and obtains a simple and practical interpolation correction formula by using a polynomial fitting function. Experiments show that: the algorithm presented herein has a higher accuracy than a single window. Meanwhile, the practical problems of complex harmonic environment, fundamental wave frequency fluctuation, white noise pollution and the like can be overcome, the application of an embedded system is easy, and the embedded system has certain application value.
Claims (10)
1. The high-frequency harmonic analysis method based on the MSD mixed convolution window is characterized by comprising the following steps of:
(1) Sampling a voltage and current signal x (n) to be measured in the wireless charging process, wherein the sampling rate of the signal is f s Obtaining N-point sampling data after analog-to-digital conversion;
(2) Constructing an MSD window function and performing mixed convolution operation to obtain a mixed convolution window;
(3) Adding MSD mixed convolution window to the sampled N-point sampling data to obtain FFT spectrum;
(4) Determining four spectral lines in the four-spectral line interpolation based on the FFT spectrum;
(5) And obtaining the frequency amplitude and the phase of the corrected fundamental wave and each subharmonic through interpolation operation.
2. The method for high-frequency harmonic analysis based on MSD mixed convolution window according to claim 1, wherein the method for constructing MSD window function in step (2) is:
selecting MSD windows of different lengths according to equation (1), i.e. w 1 (m 1 )，w 2 (m 2 )，...，w p (m p )，
Corresponding length M 1 ，M 2 ，...，M p 。
3. The method for high-frequency harmonic analysis based on the MSD mixed convolution window according to claim 1, wherein the method for determining the mixed convolution window in step (2) is as follows:
the mixed convolution window function time domain obtained after carrying out convolution operation on MSD cosine windows with different lengths is as follows:
0 s are added at the first segment or the tail end of the sequence, so that the length of the mixed convolution window
Performing FFT (fast Fourier transform) on the time domain signal convolution result of the formula (1) to obtain a frequency domain signal convolution result of a p-order mixed convolution window of the formula (3):
4. the method for high-frequency harmonic analysis based on the MSD mixed convolution window according to claim 1, wherein the method for obtaining the FFT spectrum based on the mixed convolution window in step (3) comprises:
p-order mixed convolution window w with length N after discrete signal sampling hp (n) obtaining a windowed signal:
x wp (n)＝x(n)w hp (n) (4)
fourier transforming equation (3) to obtain the frequency domain of the windowed signal:
wherein the frequency of the sampling signal x (n) is f 0 Amplitude is A, initial phase isNeglecting the effect of side lobes at the negative frequency point, the method can obtain:
bringing formula (2) into availability:
the window function expressions for each participating convolution are:
the mixed convolution window expression is obtained from equation (8):
5. the method for high-frequency harmonic analysis based on the MSD mixed convolution window according to claim 1, wherein the method for determining four spectral lines in the four spectral line interpolation in the step (4) is as follows:
selecting spectral line k with maximum amplitude near peak spectral point f in FFT spectrum with frequency close to peak spectral point f after grid signal x (n) windowing 2 、k 2 The next largest spectral line k 1 、k 4 Let the amplitude of the two phases be y respectively 1 、y 2 、y 3 、y 4 I.e. y 1 ＝|X wp (k 1 )|、y 2 ＝|X wp (k 2 )|、y 3 ＝|X wp (k 3 )|、y 4 ＝|X wp (k 4 )|，
The corresponding magnitudes for each spectral line are as follows:
/>
6. the method for analyzing high-frequency harmonics based on the MSD mixed convolution window according to claim 1, wherein the method for determining the frequency amplitude and phase of the modified fundamental wave and each subharmonic in the step (5) is as follows:
let δ=k-k 2 -0.5, since 0.ltoreq.k-k 2 If not more than 1, delta is less than-0.5, 0.5]Establishing four spectral line interpolation to solve the offset delta,
i.e.Gamma is a function of delta, and gamma=h (delta), and the offset is obtained by solving an inverse function of the gamma=h (delta) through least square fitting:
δ＝H -1 (γ) (12)
fitting by using a polynomial approximation method to obtain:
δ≈L(γ)＝a 1 γ+a 3 γ 3 +…+a 2q+1 γ 2q+1 (13)
wherein a is 1 ，a 3 ，…，a 2q+1 Odd term times.
The frequency correction formula according to the delta-obtainable signal is:
f 0 ＝kΔf＝(k 2 +0.5+δ)f s /N (14)
the phase correction formula of the signal is:
the amplitude correction formula of the signal is:
when N is large, the magnitude correction formula is expressed by a fitting formula τ (δ) as:
where τ (δ) is an even function, the correction polynomial of the magnitude is:
wherein a is 0 ，a 2 ，…，a 2q Is an even term coefficient.
7. The method of claim 1, wherein the polynomial approximation is a fitting of an inverse function offset using a polyfit function of Matlab.
8. A high-frequency harmonic analysis system based on MSD mixed convolution window is characterized by comprising a data acquisition module, a windowing processing module and an output module,
the data acquisition module acquires wireless charging current and voltage data of the electric automobile and changes the voltage and current data into discrete signals;
the windowing processing module performs windowing processing on the acquired voltage and current data to obtain a windowed FFT spectrum;
and the output module obtains interpolation coefficients from the data by adopting a four-spectral-line interpolation algorithm, and corrects the data to obtain corrected voltage current phase amplitude and frequency.
9. A computing device comprising a memory for storing instructions for a computer to perform the analysis method of any one of claims 1-7 and a processor for executing instructions for the computer-executable analysis method of any one of claims 1-7.
10. A computer readable storage medium storing computer executable instructions which when executed by a processor implement the MSD hybrid convolution window-based high frequency harmonic analysis method of any one of claims 1 to 7.
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